An Introduction to Analytical Plane Geometry

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Deighton, Bell, & Company, 1867 - Geometry, Analytic - 272 pages
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Page 105 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 88 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 42 - A point moves so that the difference of the squares of its distances from (3, 0) and (0, — 2) is always equal to 8.
Page 99 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Page 33 - Divide by the square root of the sum of the squares of the coefficients of x and y.
Page 232 - Given four points on a conic, the locus of the pole of a given line is a conic passing through the four points (Chap.
Page 102 - In this equation n is the tangent of the angle which the line makes with the axis of abscissae, and B is the intercept on this axis from the origin.
Page 7 - The area of a triangle is equal to half the product of two sides and the sine of the included angle.
Page 182 - If a rectangular hyperbola circumscribe a triangle, the locus of its centre is the
Page 101 - The curve y2 = kqx passes through the origin and the line x = 0 is the tangent at the origin. (Art. 100.) For every positive value of x there are two values of y, equal in magnitude and of opposite sign: thus the curve is symmetrical with respect to the axis of x. Also if x be negative, y is impossible. Thus the curve lies wholly on the Ox side of the axis of y. If x be infinitely great, so is y. Thus the curve is of infinite size. 106. To find the equation to the tangent at the point x'y'.

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